Category Archives: Basic

Gravity has a good sense of humour. On the one hand, it’s the weakest force we know. The upward push of your chair is more than enough to counteract the pull of the entire planet! Yet gravity has an ace up its sleeve – unlike all other forces, it’s always attractive. For larger objects, the other forces start bickering and cancelling out. But gravity just keeps on getting stronger, until it’s impossible to escape – a black hole!

As a theoretical physicist, I tend to carry a black hole whenever I’m travelling.

My “black hole” bucket.

As you can see, the top of this bucket is the surface of a black hole, otherwise known as the event horizon. When I release water from a glass above the black hole, it is attracted to the black hole, and falls inexorably towards it, never to be seen again.

This water is doomed!

Okay, I suppose my bucket isn’t a real black hole. After all, it’s the gravity of the Earth that pulls the water in. And light can definitely escape because I can see inside it! But it does accurately represent the bending of space and time. Albert Einstein taught us that everything in the universe rolls around on the cosmic quilt of spacetime, like balls on an elastic sheet. A heavy ball distorts the sheet, creating my black hole bucket.

You might not feel too threatened by black holes – after all, the nearest one is probably 8 billion billion miles away. But in actual fact you could be falling into a black hole right now without noticing! Turns out that for a large enough black hole, the event horizon is so far away that gravity there is very weak. So there’s no reason why you should experience anything special.

Maybe we, and all this, have just passed the point of no return…

This disturbing fact has an unexpected consequence from the microscopic world of quantum mechanics. Every quantum theory must have a single vacuum, essentially the most boring and lazy state of affairs. If I stand still the vacuum is just empty space. But as soon as I start accelerating something weird happens. Particles suddenly appear from nowhere!

What does that mean for our black hole? Well if you’re not falling in, you must be accelerating away to oppose the huge pull of gravity! This means that you should see the black hole glowing with particles called Hawking radiation. Remember my black hole full of water? Well, you haven’t fallen in. And that means I have to cover you with Hawking radiation!

It’s confetti! Um, I mean Hawking radiation.

Luckily for your computer, the Hawking confetti that came out isn’t the same as the water that went in. From your perspective the water has simply disappeared! Exactly the same thing seems to happen for real black holes.

This black hole magic trick has become infamous among scientists, resisting all efforts at explanation. But a solution might be at hand, courtesy of Hawking himself! What if you could slightly change the vacuum every time something dropped into the black hole? Then, if you’re very careful, you might just be able to reconstruct the original water from the confetti of Hawking radiation.

Is the event horizon a cosmic hairdresser?

Put another way, the event horizon takes a lock of soft hair from every passing particle as a memento of its existence. This information is eventually carried off by Hawking’s magic particles, reminding us of what we’d lost. It remains for soft experts, like myself, to work out the exact details.

This post is based on a talk given for the Famelab competition. You can read the full paper by Stephen Hawking, Malcolm Perry and Andy Strominger here.

Next month, I’m running a day-long conference here at QMUL. The meeting is intended to give early career researchers the chance to seek possible collaborations. Despite living in this globalised age, all too often PhD students and postdocs are restricted to working with faculty members in their current institution. This is no surprise – at the conferences and meetings where networking opportunities arise, we’re usually talking about completed work, rather than discussing new problems.

We’re shaking up the status quo by asking our participants to speak about ongoing research, and in particular to outline roadblocks where they need input from theorists with different expertise. What’s more, we’re throwing together random teams for speed collaboration sessions on the issues presented, getting the ball rolling for possible acknowledgements and group projects. We’re extremely fortunate to have the inspirational Fernando Alday as our guest speaker, a serial collaborator himself.

The final novelty of this conference comes in digital form. The conference website doubles as a social network, making it easy to keep track of your connections and maintain interactions after the meeting. We hope to generate good content on the site during the day, where some participants will be invited to act as scribes and note down any interesting ideas that arise. This way, there’ll be a valuable and evolving database of ideas ready for future collaborations to draw on.

Over to you! If you’re doing a PhD or a postdoc in the UK, or you know someone who is, send them a link to the website

18 months ago I embarked on a PhD, fresh-faced and enthusiastic. I was confident I could learn enough to understand research at the coal-face. But when faced with the prospect of producing an original paper, I was frankly terrified. How on earth do you turn vague ideas into concrete results?

In retrospect, my naive brain was crying out for an algorithm. Nowadays we’re so trained to jump through examination hoops that the prospect of an open-ended project terrifies many. Here’s the bad news – there’s no well-marked footpath leading from academic interest to completed write-up.

So far, so depressing. Or is it? After all, a PhD is meant to be a voyage of discovery. Sure, if I put you on a mountain-top with no map you’d likely be rather scared. But there’s also something exhilarating about striking out into the unknown. Particularly, that is, if you’re armed with a few orienteering skills.

Where next?

I’m about to finish my first paper. I can’t and won’t tell you how to write one! Instead, here’s a few items for your kit-bag on the uncharted mountain of research. With these in hand, you’ll be well-placed to forge your own route towards the final draft.

Your Supervisor

Any good rambler takes a compass. Your supervisor is your primary resource for checking direction. Use them!

Yes, I really am going to keep pursuing this analogy.

It took me several months (and one overheard moan) to start asking for pointers. Nowadays, if I’m completely lost for more than a few hours, I’ll seek guidance.

2. Your Notes

You start off without a map. It’s tempting to start with unrecorded cursory reconnaissance, just to get the lie of the land. Although initially speedy, you have to be super-disciplined lest you go too far and can’t retrace your steps. You’d be better off making notes as you go. Typesetting languages and subversion repositories can help you keep track of where you are.

Don’t forget to make a map!

Your notes will eventually become your paper – hence their value! But there’s a balance to be struck. It’s tempting to spend many hours on pretty formatting for content which ends up in Appendix J. If in doubt, consult your compass.

3. Your Colleagues

Some of them have written papers before. All of them have made research mistakes. Mutual support is almost as important in a PhD programme as on a polar expedition! But remember that research isn’t a race. If your colleague has produced three papers in the time it’s taken you to write one, that probably says more about their subfield and style of work than your relative ability.

You’ll need your colleagues just as much as Shackleton did.

4. Confidence

Aka love of failure. If you sit on top of the mountain and never move then you’ll certainly stay away from dangerous edges. But you’ll also never get anywhere! You will fail much more than you succeed during your PhD. Every time you pursue an idea which doesn’t work, you are honing in on the route which will.

Be brave! (Though maybe you should wait for the snow to melt first).

In this respect, research is much like sport – positive psychology is vital. Bottling up frustration is typically unhelpful. You’d be much better off channelling that into…

5. Not Writing Your Paper

You can’t write a paper 24/7 and stay sane. Thankfully a PhD is full of other activities that provide mental and emotional respite. My most productive days have coincided with seminars, teaching commitments and meetings. You should go to these, especially if you’re feeling bereft of motivation.

Why not join a choir?

And your non-paper pursuits needn’t be limited to the academic sphere. A regular social hobby, like sports, music or debating, can provide a much needed sense of achievement. Many PhDs I know also practice some form of religion, spirituality or meditation. Time especially set aside for mental rest will pay dividends later.

6. Literature

No, I don’t mean related papers in your field (though these are important). I’ve found fiction, particularly that with intrigue and character development, hugely helpful when I’m struggling to cross an impasse. Perhaps surprisingly, some books aimed at startups are also worth a read. A typical startup faces corporate research problems akin to academic difficulties.

Finally, remember that research is by definition iterative! You cannot expect your journey to end within a month. As you chart the territory around you, try to enjoy the freedom of exploring. Who knows, you might just spot a fascinating detour that leads directly to an unexpected paper.

My thanks to Dr. Inger Mewburn and her wonderful Thesis Whisperer blog for inspiring this post.

Thomson-Reuters has reportedly published their yearly analysis of the hottest trends in science research. Increasingly, governments and funding organisations use such documents to identify strategic priorities. So it’s profoundly disturbing that their conclusions are based on shoddy methodology and bad science!

The researchers first split recent papers into 10 broad areas, of which Physics was one. And then the problems began. According to the official document

Research fronts assigned to each of the
10 areas were ranked by total citations and the top 10 percent of the fronts in each area were extracted.

Already the authors have fallen into two fallacies. First, they have failed to normalise for the size of the field. Many fields (like Higgs phenomenology) will necessarily generate large quantities of citations due to their high visibility and current funding. Of course, this doesn’t mean that we’ve cracked naturalness all of a sudden!

Second their analysis is far too coarse-grained. Physics contains many disciplines, with vastly different publication rates and average numbers of citations. Phenomenologists publish swiftly and regularly, while theorists have longer papers with slower turnover. Experimentalists often fall somewhere in the middle. Clearly the Thomson-Reuters methodology favours phenomenology over all else.

But wait, the next paragraph seems to address these concerns. To some extent they “cherry pick” the hottest research fronts to account for these issues. According to the report

Due to the different characteristics and citation behaviors in various disciplines, some fronts are much smaller than others in terms of number of core and citing papers.

Excellent, I hear you say – tell me more! But here comes more bad news. It seems there’s no information on how this cherry picking was done! There’s no mention of experts consulted in each field. No mathematical detail about how vastly different disciplines were fairly compared. Thomson-Reuters have decided that all the reader deserves is a vague placatory paragraph.

And it gets worse. It turns out that the scientific analysis wasn’t performed by a balanced international committee. It was handed off to a single country – China. Who knows, perhaps they were the lowest bidder? Of course, I couldn’t possibly comment. But it seems strange to me to pick a country famed for its grossly flawed approach to scientific funding.

Governments need to fund science based on quality and promise, not merely quantity. Thomson-Reuters simplistic analysis is bad science at its very worst. It seems to offer intelligent information but in fact is misleading, flawed and ultimately dangerous.

All too soon we’ve reached the end of a wonderful conference. Friday morning dawned with a glimpse of perhaps the most impressive calculation of the past twelve months – Higgs production at three loops in QCD. This high precision result is vital for checking our theory against the data mountain produced by the LHC.

It was well that Professor Falko Dulat‘s presentation came at the end of the week. Indeed the astonishing computational achievement he outlined was only possible courtesy of the many mathematical techniques recently developed by the community. Falko illustrated this point rather beautifully with a word cloud.

As amplitudeologists we are blessed with a incredibly broad field. In a matter of minutes conversation can encompass hard experiment and abstract mathematics. The talks this morning were a case in point. Samuel Abreu followed up the QCD computation with research linking abstract algebra, graph theory and physics! More specifically, he introduced a Feynman diagram version of the coproduct structure often employed to describe multiple polylogs.

Dr. HuaXing Zhu got the ball rolling on the final mini-session with a topic close to my heart. As you may know I’m currently interested in soft theorems in gauge theory and gravity. HuaXing and Lance Dixon have made an important contribution in this area by computing the complete -loop leading soft factor in QCD. Maybe unsurprisingly the breakthrough comes off the back of the master integral and differential equation method which has dominated proceedings this week.

Last but by no means least we had an update from the supergravity mafia. In recent years Dr. Tristan Dennen and collaborators have discovered unexpected cancellations in supergravity theories which can’t be explained by symmetry alone. This raises the intriguing question of whether supergravity can play a role in a UV complete quantum theory of gravity.

The methods involved rely heavily on the color-kinematics story. Intriguingly Tristan suggested that the double copy connection because gauge theory and gravity could form an explanation for the miraculous results (in which roughly a billion terms combine to give zero)! The renormalizability of Yang-Mills theory could well go some way to taming gravity’s naive high energy tantrums.

There’s still some way to go before bottles of wine change hands. But it was fitting to end proceedings with an incomplete story. For all that we’ve thought hard this week, it is now that the graft really starts. I’m already looking forward to meeting in Stockholm next year. My personal challenge is to ensure that I’m among the speakers!

Particular thanks to all the organisers, and the many masters students, PhDs, postdocs and faculty members at ETH Zurich who made our stay such an enjoyable and productive one!

One of the first pieces of Bach ever recorded was August Wilhelmj’s arrangement of the Orchestral Suite in D major. Today the transcription for violin and piano goes by the moniker Air on the G String. It’s an inspirational and popular work in all it’s many incarnations, not least this one featuring my favourite cellist Yo-Yo Ma.

This morning we heard the physics version of Bach’s masterpiece. Superstrings are nothing new, of course. But recently they’ve received a reboot courtesy of Dr. David Skinner among others. The ambitwistor string is an infinite tension version which only admit right-moving vibrations! At first the formalism looks a little daunting, until you realise that many calculations follow the well-trodden path of the superstring.

Now superstring amplitudes are quite difficult to compute. So hard, in fact, that Dr. Oliver Schloterrer devoted an entire talk to understanding particular functions that emerge when scattering just strings at next-to-leading order. Mercifully, the ambitwistor string is far more well-behaved. The resulting amplitudes are rather beautiful and simple. To some extent, you trade off the geometrical aesthetics of the superstring for the algebraic compactness emerging from the ambitwistor approach.

This isn’t the first time that twistors and strings have been combined to produce quantum field theory. The first attempt dates back to 2003 and work of Edward Witten (of course). Although hugely influential, Witten’s theory was esoteric to say the least! In particular nobody knows how to encode quantum corrections in Witten’s language.

Ambitwistor strings have no such issues! Adding a quantum correction is easy – just put your theory on a donut. But this conceptually simple step threatened a roadblock for the research. Trouble was, nobody actually knew how to evaluate the resulting formulae.

Nobody, that was, until last week! Talented folk at Oxford and Cambridge managed to reduce the donutty problem to the original spherical case. This is an impressive feat – nobody much suspected that quantum corrections would be as easy as a classical computation!

There’s a great deal of hope that this idea can be rigorously extended to higher loops and perhaps even break the deadlock on maximal supergravity calculations at -loop level. The resulting concept of off-shell scattering equations piqued my interest – I’ve set myself a challenge to use them in the next 12 months!

Scattering equations, you say? What are these beasts? For that we need to take a closer look at the form of the ambitwistor string amplitude. It turns out to be a sum over the solutions of the following equations

The are just two particle invariants – encoding things you can measure about the speed and angle of particle scattering. And the are just some bonus variables. You’d never dream of introducing them unless somebody told you to! But yet they’re exactly what’s required for a truly elegant description.

And these scattering equations don’t just crop up in one special theory. Like spies in a Cold War era film, they seem to be everywhere! Dr. Freddy Cachazo alerted us to this surprising fact in a wonderfully engaging talk. We all had a chance to play detective and identify bits of physics from telltale clues! By the end we’d built up an impressive spider’s web of connections, held together by the scattering equations.

Freddy’s talk put me in mind of an interesting leadership concept espoused by the conductor Itay Talgam. Away from his musical responsibilities he’s carved out a niche as a business consultant, teaching politicians, researchers, generals and managers how to elicit maximal productivity and creativity from their colleagues and subordinates. Critical to his philosophy is the concept of keynote listening – sharing ideas in a way that maximises the response of your audience. This elusive quality pervaded Freddy’s presentation.

Following this masterclass was no mean feat, but one amply performed by my colleague Brenda Penante. We were transported to the world of on-shell diagrams – a modern alternative to Feynman’s ubiquitous approach. These diagrams are known to produce the integrand in planar $\mathcal{N}=4$ super-Yang-Mills theory to all orders! What’s more, the answer comes out in an attractive form, ripe for integration to multiple polylogarithms.

Cunningly, I snuck the word planar into the paragraph above. This approximation means that the diagrams can be drawn on a sheet of paper rather than requiring dimensions. For technical reasons this is equivalent to working in the theory with an infinite number of color charges, not just the usual we find for the strong force.

Obviously, it would be helpful to move beyond this limit. Brenda explained a decisive step in this direction, providing a mechanism for computing all leading singularities of non-planar amplitudes. By examining specific examples the collaboration uncovered new structure invisible in the planar case.

Technically, they observed that the boundary operation on a reduced graph identified non-trivial singularities which can’t be understood as the vanishing of minors. At present, there’s no proven geometrical picture of these new relations. Amazingly they might emerge from a 1,700-year-old theorem of Pappus!

Bootstraps were back on the agenda to close the session. Dr. Agnese Bissi is a world-expert on conformal field theories. These models have no sense of distance and only know about angles. Not particularly useful, you might think! But they crop up surprisingly often as approximations to realistic physics, both in particle smashing and modelling materials.

Agnese took a refreshingly rigorous approach, walking us through her proof of the reciprocity principle. Until recently this vital tool was little more than an ad hoc assumption, albeit backed up by considerable evidence. Now Agnese has placed it on firmer ground. From here she was able to “soup up” the method. The supercharged variant can compute OPE coefficients as well as dimensions.

Alas, it’s already time for the conference dinner and I haven’t mentioned Dr. Christian Bogner‘s excellent work on the sunrise integral. This charmingly named function is the simplest case where hyperlogarithms are not enough to write down the answer. But don’t just take it from me! You can now hear him deliver his talk by visiting the conference website.

Conversations

I’m very pleased to have chatted with Professor Rutger Boels (on the Lagrangian origin of Yang-Mills soft theorems and concerning the universality of subheading collinear behaviour) and Tim Olson (about determining the relative sign between on-shell diagrams to ensure cancellation of spurious poles).

Note: this post was originally written on Thursday 9th July but remained unpublished. I blame the magnificent food, wine and bonhomie at the conference dinner!

The middle day of a conference. So often this is the graveyard slot – when initial hysteria has waned and the final furlong seems far off. The organisers should take great credit that today was, if anything, the most engaging thus far! Even the weather was well-scheduled, breaking overnight to provide us with more conducive working conditions.

Integrability was our wake-up call this morning. I mentioned this hot topic a while back. Effectively it’s an umbrella term for techniques that give you exact answers. For amplitudes folk, this is the stuff of dreams. Up until recently the best we could achieve was an expansion in small or large parameters!

So what’s new? Dr. Amit Sever brought us up to date on developments at the Perimeter Institute, where the world’s most brilliant minds have found a way to map certain scattering amplitudes in dimensions onto a dimensional model which can be exactly solved. More technically, they’ve created a flux tube representation for planar amplitudes in super-Yang-Mills, which can then by solved using spin chain methods.

The upshot is that they’ve calculated particle scattering amplitudes to all values of the (‘t Hooft) coupling. Their method makes no mention of Feynman diagrams or string theory – the old-fashioned ways of computing this amplitude for weak and strong coupling respectively. Nevertheless the answer matches exactly known results in both of these regimes.

There’s more! By putting their computation under the microscope they’ve unearthed unexpected new physics. Surprisingly the multiparticle poles familiar from perturbative quantum field theory disappear. Doing the full calculation smoothes out divergent behaviour in each perturbative term. This is perhaps rather counterintuitive, given that we usually think of higher-loop amplitudes as progressively less well-behaved. It reminds me somewhat of Regge theory, in which the UV behaviour of a tower of higher spin states is much better than that of each one individually.

The smorgasbord of progress continued in Mattias Wilhelm’s talk. The Humboldt group have a completely orthogonal approach linking integrability to amplitudes. By computing form factors using unitarity, they’ve been able to determine loop-corrections to anomalous dimensions. Sounds technical, I know. But don’t get bogged down! I’ll give you the upshot as a headline – New Link between Methods, Form Factors Say.

Coffee consumed, and it was time to get colorful. You’ll hopefully remember that the quarks holding protons and neutrons together come in three different shades. These aren’t really colors that you can see. But they are internal labels attached to the particles which seem vital for our theory to work!

About 30 years ago, people realised you could split off the color-related information and just deal with the complicated issues of particle momentum. Once you’ve sorted that out, you write down your answer as a sum. Each term involves some color stuff and a momentum piece. Schematically

What they didn’t realise was that you can shuffle momentum dependence between terms to force the kinematic parts to satisfy the same equations as the color parts! This observation, made back in 2010 by Zvi Bern, John Joseph Carrasco and Henrik Johansson has important consequences for gravity in particular.

Why’s that? Well, if you arrange your Yang-Mills kinematics in the form suggested by those gentlemen then you get gravity amplitudes for free. Merely strip off the color bit and replace it by another copy of the kinematics! In my super-vague language above

Dr. John Joseph Carrasco himself brought us up to date with a cunning method of determining the relevant kinematic choice at loop level. I can’t help but mention his touching modesty. Even though the whole community refers to the relations by the acronym BCJ, he didn’t do so once!

Before that Dr. Donal O’Connell took us on an intriguing detour of solutions to classical gravity theories with an appropriate dual Yang-Mills theory, obtainable via a BCJ procedure. The idea is beautiful, and seems completely obvious once you’ve been told! Kudos to the authors for thinking of it.

After lunch we enjoyed a well-earned break with a hike up the Uetliberg mountain. I learnt that this large hill is colloquially called Gmuetliberg. Yvonne Geyer helpfully explained that this is derogatory reference to the tame nature of the climb! Nevertheless the scenery was very pleasant, particularly given that we were mere minutes away from the centre of a European city. What I wouldn’t give for an Uetliberg in London!

Evening brought us to Heidi and Tell, a touristic yet tasty burger joint. Eager to offset some of my voracious calorie consumption I took a turn around the Altstadt. If you’re ever in Zurich it’s well worth a look – very little beats medieval streets, Alpine water and live swing music in the evening light.

Conversations

It was fantastic to meet Professor Lionel Mason and discuss various ideas for extending the ambitwistor string formalism to form factors. I also had great fun chatting to Julio Martinez about linking CHY and BCJ. Finally huge thanks to Dr. Angnis Schmidt-May for patiently explaining the latest research in the field of massive gravity. The story is truly fascinating, and could well be a good candidate for a tractable quantum gravity model!

Erratum: An earlier version of this post mistakenly claimed that Chris White spoke about BCJ for equations of motion. Of course, it was his collaborator Donal O’Connell who delivered the talk. Many thanks to JJ Carrasco for pointing out my error!

It’s conference season! I’m hanging out in very warm Zurich with the biggest names in my field – scattering amplitudes. Sure it’s good fun to be outside the office. But there’s serious work going on too! Research conferences are a vital forum for the exchange of ideas. Inspiration and collaboration flow far more easily in person than via email or telephone. I’ll be blogging the highlights throughout the week.

Monday | Morning Session

To kick-off we have some real physics from the Large Hadron Collider! Professor Nigel Glover‘s research provides a vital bridge between theory and experiment. Most physicists in this room are almost mathematicians, focussed on developing techniques rather than computing realistic quantities. Yet the motivation for this quest lie with serious experiments, like the LHC.

We’re currently entering an era where the theoretical uncertainty trumps experimental error. With the latest upgrade at CERN, particle smashers will reach unprecedented accuracy. This leaves us amplitudes theorists with a large task. In fact, the experimentalists regularly draw up a wishlist to keep us honest! According to Nigel, the challenge is to make our predictions twice as good within ten years.

At first glance, this 2x challenge doesn’t seem too hard! After all Moore’s Law guarantees us a doubling of computing power in the next few years. But the scale of the problem is so large that more computing power won’t solve it! We need new techniques to get to NNLO – that is, corrections that are multiplied by the square of the strong coupling. (Of course, we must also take into account electroweak effects but we’ll concentrate on the strong force for now).

Nigel helpfully broke down the problem into three components. Firstly we must compute the missing higher order terms in the amplitude. The start of the art is lacking at present! Next we need better control of our input parameters. Finally we need to improve our model of how protons break apart when you smash them together in beams.

My research helps in a small part with the final problem. At present I’m finishing up a paper on subleading soft loop corrections, revealing some new structure and developing a couple of new ideas. The hope is that one day someone will use this to better eliminate some irritating low energy effects which can spoil the theoretical prediction.

In May, I was lucky enough to meet Bell Labs president Dr. Marcus Weldon in Murray Hill, New Jersey. He spoke about his vision for a 10x leap forward in every one of their technologies within a decade. This kind of game changing goal requires lateral thinking and truly new ideas.

We face exactly the same challenge in the world of scattering amplitudes. The fact that we’re aiming for only a 2x improvement is by no means a lack of ambition. Rather it underlines that problem that doubling our predictive power entails far more than a 10x increase in complexity of calculations using current techniques.

I’ve talked a lot about accuracy so far, but notice that I haven’t mentioned precision. Nigel was at pains to distinguish the two, courtesy of this amusing cartoon.

Why is this so important? Well, many people believe that NNLO calculations will reduce the renormalization scale uncertainty in theoretical predictions. This is a big plus point! Many checks on known NNLO results (such as W boson production processes) confirm this hunch. This means the predictions are much more precise. But it doesn’t guarantee accuracy!

To hit the bullseye there’s still much work to be done. This week we’ll be sharpening our mathematical tools, ready to do battle with the complexities of the universe. And with that in mind – it’s time to get back to the next seminar. Stay tuned for further updates!

Update | Monday Evening

Only time for the briefest of bulletins, following a productive and enjoyable evening on the roof of the ETH main building. Fantastic to chat again to Tomek Lukowski (on ambitwistor strings), Scott Davies (on supergravity 4-loop calculations and soft theorems) and Philipp Haehnal (on the twistor approach to conformal gravity). Equally enlightening to meet many others, not least our gracious hosts from ETH Zurich.

My favourite moment of the day came in Xuan Chen’s seminar, where he discussed a simple yet powerful method to check the numerical stability of precision QCD calculations. It’s well known that these should factorize in appropriate kinematic regions, well described by imaginatively named antenna functions. By painstakingly verifying this factorization in a number of cases Xuan detected and remedied an important inaccuracy in a Higgs to 4 jet result.

Of course it was a pleasure to hear my second supervisor, Professor Gabriele Travaglini speak about his latest papers on the dilatation operator. The rederivation of known integrability results using amplitudes opens up an enticing new avenue for those intrepid explorers who yearn to solve super-Yang-Mills!

Finally Dr. Simon Badger‘s update on the Edinburgh group’s work was intriguing. One challenge for NNLO computations is to understand 2-loop corrections in QCD. The team have taken an important step towards this by analysing 5-point scattering of right-handed particles. In principle this is a deterministic procedure: draw some pictures and compute.

But to get a compact formula requires some ingenuity. First you need appropriate integral reduction to identify appropriate master integrals. Then you must apply KK and BCJ relations to weed out the dead wood that’s cluttering up the formula unnecessarily. Trouble is, both of these procedures aren’t uniquely defined – so intelligent guesswork is the order of the day!

That’s quite enough for now – time for some sleep in the balmy temperatures of central Europe.

I spent this morning singing a Sunday service at St. George’s Church in Borough. An odd occupation for a scientist perhaps, especially given the high profile of several atheist researchers! Yet a large number of scientists see no contradiction between faith and science. In fact, my Christian faith is only deepened by my fascination with the natural world.

Picture a scientist. Chances are you’ve already got in your mind a geeky, rational person, calibrating a precise experiment or poring over a dry mathematical formula! As with any stereotype, it has it’s merits. But it misses a vital quality in research – imagination.

To succeed as a scientist, you must be creative above all else. It’s no use just learning experimental techniques or memorising formulae. Every new idea must necessarily start off as a fantasy. Great painters are not merely lauded for their 10,000 hours of practice with a paintbrush. It is their capacity to conceive and relay vivid scenes which ensures their place in history. And so it is with science.

So why are scientists seen as cold and calculating and exact, rather than passionate and original? The problem lies in education. While young children are encouraged to express themselves in Literacy, Numeracy is all too often a trudge through tedious and predictable sums. In “arts” subjects, questions are a magical tool enabling discussion, debate and opinion. In “sciences” they merely distinguish right from wrong.

After 15 years of schooling, no wonder the stereotype is embedded! As a teenager, I very nearly ditched the sciences in favour of subjects where expression was free and original arguments rewarded. I’m eternally thankful to my teachers, parents and bookshelf for convincing me that the curriculum was utterly unrepresentative of real science.

So what’s to be done. For any budding scientists out there, your best bet is to read some books. Not your school textbooks – chances are they are dull as ditchwater and require no creative input at all. I mean books written by real life mathematicians, physicists, biologists… These will give you an insight into the imagination that drives research, the contentious debates and the lively exchanges of ideas.

You might not understand everything, but that’s the whole point – science is about the unknown, just as much as art or faith. It is exactly this point which we must evangelise again and again. Perhaps then fewer people will write negative reviews criticising science for being complex, poetic and beautiful.

As a wider society, we can take action too! We must demand better science teaching from a young age. Curricula should emphasise problem solving over knowledge, ideas over techniques and originality over regurgitation. This is already the mantra for many traditionally “artistic” discplines. It must be the battle cry for scientists also!

A better approach to science would democratize opportunity for the next generation. No longer will the relative creativity of girls be arbitrarily punished – an approach which can only discourage women from entering science in the long run. No longer will there be a tech skills gap threatening to undermine the thriving software industry. The UK has a uniquely privileged scientific pedigree. For future equality, economy and diversity, we must use it.

In the service this morning Fr Jonathan Sedgwick talked of the danger of applying scientific laws to the world at large. The concepts of “cause and effect” and “zero sum games” may well work in vacuo, but they are artificial and burdensome when applied to interpersonal relationships. Quite right – as Christians we must question these human rules, and look for a divine inspiration to guide our lives!

But this is also precisely what we must do as scientists. A good scientist always questions their models, constantly listening for the voice of intuition. For science – like our own existence – is ever changing. And it’s our job to search for the way, the truth and the life.

My thanks to Margaret Widdess, who prepared me for confirmation two years ago at St. Catharine’s College, Cambridge and with whom I first talked deeply about the infinity of science and faith.

I’ve just finished writing a lecture course for SEPnet, a consortium of leading research universities in the South East of Britain. The course comprises a series of webcasts introducing Mathematica – check it out here!

Although the course starts from the basics, I hope it’ll be useful to researchers at all levels of academia. Rather than focussing on computations, I relay the philosophy of Mathematica. This uncovers some tips, tricks and style maxims which even experienced users might not have encountered.

I ought to particularly thank the Mathematica Summer School for inspiring this project, and demonstrating that Mathematica is so much more than just another programming language. If you’re a theorist who uses computer algebra on a daily basis, I thoroughly recommend you come along to the next edition of the school in September.